The Premier League outfit have been keeping a close eye on the Serbian’s development over the last few years and their scouts were in attendance on Saturday as Benfica beat Rio Ave.
Reports claim that Arsenal did make an informal approach to the Portuguese side over the summer, but they were initially put off by his £52.5million release clause.
Zivkovic joined Benfica from Partizan Belgrade in 2016 on a free transfer, penning a five-year contract, having made his full debut for the Serbian club as a 17-year-old.
Benfica have a reputation for driving a hard deal, having sold on the likes of Victor Lindelof and Renato Sanches for large fees in recent years, and Arsenal are unlikely to be able to negotiate them down if they do make an official bid next summer.
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.
Southend manager Chris Powell led the applause for Jason Demetriou after the right-back scored twice in the 3-1 win against Portsmouth at Roots Hall.
Morecambe boss Jim Bentley was the happier manager after Gregg Wylde's 90th-minute strike earned his side a point in their 1-1 draw with Forest Green.
Manager Gareth Ainsworth described Wycombe's 2-0 win at Cheltenham as a thoroughly professional performance.
Skipper Richard Wood scored the winner just before half time as in-form Rotherham pulled off a 1-0 victory at League One leaders Shrewsbury.